What is the integral of (x^2)/(sqrt(a^2+b^2)) ?

The integral of (x^2)/(sqrt(a^2+b^2)) is (x^3)/(3sqrt(a^2+b^2))+C

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integral of (x^2)/(sqrt(a^2+b^2))

\int \frac{x ^{2}}{a ^{2} + b ^{2}} d x

\frac{x ^{3}}{3 a ^{2} + b ^{2}} + C

Solution steps

\int \frac{x ^{2}}{a ^{2} + b ^{2}} d x

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= \frac{1}{a ^{2} + b ^{2}} \cdot \int x^{2} d x

Apply the Power Rule

: \frac{x ^{3}}{3}

= \frac{1}{a ^{2} + b ^{2}} \cdot \frac{x ^{3}}{3}

Simplify

\frac{1}{a ^{2} + b ^{2}} \cdot \frac{x ^{3}}{3} : \frac{x ^{3}}{3 a ^{2} + b ^{2}}

= \frac{x ^{3}}{3 a ^{2} + b ^{2}}

Add a constant to the solution

= \frac{x ^{3}}{3 a ^{2} + b ^{2}} + C

\int \frac{x ^{2} - x}{x ^{3} - 6 x ^{2} + 11 x - 6} d x

\int_{0}^{5} \frac{4 t}{( t - 6 ) ^{2}} d t

\int \frac{( 4 u ^{2} - 8 )}{2 u ^{2} + 1} d u

\frac{d}{d x} (\frac{x ^{2}}{4 - x ^{2}})

- \frac{24}{x ^{4}}

What is the integral of (x^2)/(sqrt(a^2+b^2)) ?
The integral of (x^2)/(sqrt(a^2+b^2)) is (x^3)/(3sqrt(a^2+b^2))+C